Question

The sum of $\frac{1}{2} + \frac{1}{3}.\frac{1}{2^{3}} + \frac{1}{5}.\frac{1}{2^{5}} + .....\infty$ is.

• A. $\log_{e}\sqrt{\frac{3}{2}}$
• B. $\log_{e}\sqrt{3}$
• C. $\log_{e}\sqrt{\frac{1}{2}}$
• D. $\log_{e}3$

Answer 1

Answer: (B)

$\log_{e}\sqrt{3}$

Answer 2

Sum of $\frac{1 - e^{y}}{3}$

= $(1 - e^{y})^{1/3}(1 - e^{y})^{3}$

= $\frac{e^{2} + 1}{2e} =$.